Singular solutions of the Yamabe problem in the Heisenberg group and their bifurcation

We prove the existence of a homogeneous singular solution of the crit- ical equation −∆Hn u = u Q+2 Q−2 on the Heisenberg group Hn, where Q is the homogeneous dimension. In order to do this, we introduce a suitable concept of normal curvature for hypersurfaces. Furthermore we study the bifurcation of non-homogeneous solutions from the homogeneous one.